Nuprl Lemma : decidable__list-match-ext
∀[A,B:Type]. ∀[R:A ⟶ B ⟶ ℙ].
((∀a:A. ∀b:B. Dec(R[a;b])) ⇒ (∀as:A List. ∀bs:B List. Dec(list-match(as;bs;a,b.R[a;b]))))
Proof
Definitions occuring in Statement :
list-match: list-match(L1;L2;a,b.R[a; b]),
list: T List,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
eq_int: (i =z j),
btrue: tt,
it: ⋅,
bfalse: ff,
subtract: n - m,
ifthenelse: if b then t else f fi ,
spreadn: spread4,
decidable__list-match,
decidable_functionality,
decidable__list-match-aux,
iff_preserves_decidability,
list_induction,
list_match-aux-nil,
list_match-aux-cons,
sq_stable_from_decidable,
decidable__exists_int_seg,
decidable__and2,
decidable__not,
decidable__assert,
decidable__implies,
decidable__false,
decidable__and,
any: any x,
sq_stable__and,
sq_stable__all,
sq_stable__not,
sq_stable__from_stable,
stable__from_decidable,
uall: ∀[x:A]. B[x],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
decidable__list-match,
lifting-strict-callbyvalue,
strict4-decide,
lifting-strict-decide,
lifting-strict-int_eq,
decidable_functionality,
decidable__list-match-aux,
iff_preserves_decidability,
list_induction,
list_match-aux-nil,
list_match-aux-cons,
sq_stable_from_decidable,
decidable__exists_int_seg,
decidable__and2,
decidable__not,
decidable__assert,
decidable__implies,
decidable__false,
decidable__and,
sq_stable__and,
sq_stable__all,
sq_stable__not,
sq_stable__from_stable,
stable__from_decidable
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry,
isectElimination,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination
Latex:
\mforall{}[A,B:Type]. \mforall{}[R:A {}\mrightarrow{} B {}\mrightarrow{} \mBbbP{}].
((\mforall{}a:A. \mforall{}b:B. Dec(R[a;b])) {}\mRightarrow{} (\mforall{}as:A List. \mforall{}bs:B List. Dec(list-match(as;bs;a,b.R[a;b]))))
Date html generated:
2018_05_21-PM-00_48_33
Last ObjectModification:
2018_05_19-AM-06_51_13
Theory : list_1
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